Studying symmetries of structures, like graphs, helps us understand their nature and properties. The mathematical theory of symmetry has been classically associated with groups. Lately it is believed that total symmetries may be too restrictive in some situations. Thus relaxing some of the conditions leads to the concept of partial symmetries that may reveal more information about the graph. Partial symmetries are algebraically associated with inverse monoids.
The aim of the theses is to study partial symmetries of certain classes of graphs, for instance trees, and describing their algebraic representations by inverse monoids.
doc. RNDr. Tatiana Jajcayová, PhD.